U.S. patent number 8,358,141 [Application Number 12/465,022] was granted by the patent office on 2013-01-22 for analytical scanning evanescent microwave microscope and control stage.
This patent grant is currently assigned to The Regents of the University of California. The grantee listed for this patent is Fred Duewer, Chen Gao, Yalin Lu, Xiao-Dong Xiang, Hai Tao Yang. Invention is credited to Fred Duewer, Chen Gao, Yalin Lu, Xiao-Dong Xiang, Hai Tao Yang.
United States Patent |
8,358,141 |
Xiang , et al. |
January 22, 2013 |
Analytical scanning evanescent microwave microscope and control
stage
Abstract
A scanning evanescent microwave microscope (SEMM) that uses
near-field evanescent electromagnetic waves to probe sample
properties is disclosed. The SEMM is capable of high resolution
imaging and quantitative measurements of the electrical properties
of the sample. The SEMM has the ability to map dielectric constant,
loss tangent, conductivity, electrical impedance, and other
electrical parameters of materials. Such properties are then used
to provide distance control over a wide range, from to microns to
nanometers, over dielectric and conductive samples for a scanned
evanescent microwave probe, which enable quantitative non-contact
and submicron spatial resolution topographic and electrical
impedance profiling of dielectric, nonlinear dielectric and
conductive materials. The invention also allows quantitative
estimation of microwave impedance using signals obtained by the
scanned evanescent microwave probe and quasistatic approximation
modeling. The SEMM can be used to measure electrical properties of
both dielectric and electrically conducting materials.
Inventors: |
Xiang; Xiao-Dong (Danville,
CA), Gao; Chen (Hefei, CN), Duewer; Fred
(Albany, CA), Yang; Hai Tao (Albany, CA), Lu; Yalin
(Chelmsford, MA) |
Applicant: |
Name |
City |
State |
Country |
Type |
Xiang; Xiao-Dong
Gao; Chen
Duewer; Fred
Yang; Hai Tao
Lu; Yalin |
Danville
Hefei
Albany
Albany
Chelmsford |
CA
N/A
CA
CA
MA |
US
CN
US
US
US |
|
|
Assignee: |
The Regents of the University of
California (Oakland, CA)
|
Family
ID: |
40765916 |
Appl.
No.: |
12/465,022 |
Filed: |
May 13, 2009 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20090302866 A1 |
Dec 10, 2009 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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09608311 |
Jun 23, 2009 |
7550963 |
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09158037 |
Jan 16, 2001 |
6173604 |
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08717321 |
Oct 13, 1998 |
5821410 |
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60141698 |
Jun 30, 1999 |
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60059471 |
Sep 22, 1997 |
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Current U.S.
Class: |
324/635;
324/754.23 |
Current CPC
Class: |
G01Q
60/22 (20130101) |
Current International
Class: |
G01R
27/04 (20060101); G01R 31/308 (20060101) |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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547968 |
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Jun 1993 |
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EP |
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971227 |
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Jan 2000 |
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EP |
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Other References
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Society), Analytical Chemistry, vol. 68, No. 12, Jun. 15, 1996, pp.
815R-230R. cited by applicant .
Martin et al., Controlling and Tuning Strong Optical Field
Gradients at a Local Probe Microscope Tip Apex, American Institute
of Physics, Feb. 10, 1997, pp. 705-707. cited by applicant .
Hecht et al., Facts and Artifacts in Near-Field Optical Microscopy,
American Institute of Physics, Mar. 15, 1997, pp. 2492-2498. cited
by applicant .
Quidant et al., Sub-Wavelength Patterning of the Optical
Near-Field, OSA, Jan. 26, 2004, vol. 12, pp. 282-287. cited by
applicant .
Zenhausern et al., Apertureless Near-Field Optical Microscope,
Applied Physics Letters, vol. 65, No. 13, pp. 1623-1625, Sep. 1994.
cited by applicant .
Bordoni et al., A Microwave Scanning Surface Harmonic Microscope
Using a Re-Entrant Resonant Cavity, Meas. Sci. Technol. 6 (1995),
pp. 1208-1214. cited by applicant .
Anlage et al., Near-Field Microwave Microscopy of Materials
Properties, University of Maryland, Apr. 2000, pp. 1-31. cited by
applicant .
Gasper et al., An S-Band Test Cavity for a Field Emission Based
RF-Gun, Germany, pp. 1471-1473. cited by applicant .
Henning et al., Scanning Probe Microscopy for 2-D Semiconductor
Dopant Profiling and Device Failure Analysis, Materials Science and
Engineering B42, Thayer School of Engineering, NH, USA, pp. 88-98,
1996. cited by applicant .
Said et al., Heterodyne Electrostatic Force Microscopy Used as a
New Non-Contact Test Technique for Integrated Circuits, University
of Manitoba, Canada, IEEE, 1995, pp. 483-488. cited by applicant
.
Gabriel et al., Use of Time Domain Spectroscopy for Measuring
Dielectric Properties with a Coaxial Probe, J. Phys. E: Sci.
Instrum. 19 (1986), pp. 843-846. cited by applicant .
Kraszewski et al., Microwave Resonant Cavities for Sending Moisture
and Mass of Single Seeds and Kernels, 1992 Asia-Pacific Microwave
Conference, Adelaide, pp. 555-558. cited by applicant .
Derray et al., Dielectric Probe for Permittivity and Permiability
Measurements at Low Microwave Frequencies, 1992 IEEE MTT-S Digest,
pp. 1557-1560. cited by applicant .
Misra, D., A Quasi-Static Analysis of Open-Ended Coaxial Lines,
IEEE Transactions on Microwave Theory and Techniques, vol. MTT-35,
No. 10, Oct. 1987, pp. 925-928. cited by applicant.
|
Primary Examiner: Patel; Paresh
Attorney, Agent or Firm: Fliesler Meyer LLP
Government Interests
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
This invention was made with U.S. Government support under Contract
No. DE-AC03-76SF00098 between the U.S. Department of Energy and the
University of California for the operation of Lawrence Berkeley
Laboratory. The U.S. Government may have certain rights in this
invention.
Parent Case Text
CLAIM OF PRIORITY
This application is a division of U.S. patent application Ser. No.
09/608,311 filed Jun. 30, 2000, now U.S. Pat. No. 7,550,963 issued
Jun. 23, 2009, which claims the benefit of U.S. Provisional
Application No. 60/141,698 filed Jun. 30, 1999, and is a
continuation-in-part of U.S. patent application Ser. No. 09/158,037
filed Sep. 22, 1998, now U.S. Pat. No. 6,173,604 issued Jan. 16,
2001, which claims the benefit of U.S. Provisional Application No.
60/059,471, filed Sep. 22, 1997 and which is a continuation-in-part
of U.S. patent application Ser. No. 08/717,321 filed Sep. 20, 1996,
now U.S. Pat. No. 5,821,410 issued Oct. 13, 1998.
Claims
We claim:
1. A method for using a scanning evanescent microwave probe to
determine electrical properties of a sample, said probe having a
tip extending from a coaxial or transmission line resonator,
comprising: measuring variation in resonant frequency and quality
factor of said resonator resulting from interaction of said tip and
said sample; wherein said tip-sample interaction appears as
equivalent complex tip-sample capacitance; and wherein said
effective complex tip-sample capacitance, C.sub.tip-sample is
determined according to C.sub.tip-sample =C.sub.r+C.sub.i, wherein
C.sub.r and C.sub.i are the real and imaginary components of the
tip-sample capacitance, respectively,
.DELTA..times..times..times..times..DELTA..times..times..times..times..DE-
LTA..times..times..DELTA..times..times..DELTA..times..times.
##EQU00048## and f.sub.0 and Q.sub.0 are the unloaded resonant
frequency and quality factor, respectively.
2. A method as recited in claim 1, wherein said measuring of said
variation in resonant frequency and quality factor of said
resonator comprises: obtaining signal from an I/Q mixer; and
determining resonant frequency and quality factor as a function of
said signals from said I/Q mixer.
3. A method as recited in claim 1, further comprising: measuring
probe parameters selected from the group consisting of resonant
frequency shift and quality factor shift, wherein the resonant
frequency shift and the quality factor shift results from an
interaction between the sample and an evanescent electromagnetic
field emitted from said probe.
4. The method for measuring an electromagnetic property according
to claim 3, wherein the measurement is made using quasistatic
approximation modeling.
5. A method for using a scanning evanescent microwave probe to
determine electrical properties of a sample, said probe having a
tip extending from a coaxial or transmission line resonator,
comprising: measuring variation in resonant frequency and quality
factor of said resonator resulting from interaction of said tip and
said sample; said probe having said tip extending from a microwave
cavity; positioning said sample outside said microwave cavity and
adjacent said tip; causing said tip to emit an evanescent
electromagnetic field; scanning a surface of said sample with said
tip to measure resonant frequency shift of said probe, wherein said
resonant frequency shift results from interaction between said
sample and said evanescent electromagnetic field; and determining
said electrical properties and topography of said sample using the
measured resonant frequency shift.
6. A method for using a scanning evanescent microwave probe to
determine electrical properties of a sample, said probe having a
tip extending from a coaxial or transmission line resonator,
comprising: measuring variation in resonant frequency and quality
factor of said resonator resulting from interaction of said tip and
said sample; said probe having said tip extending from a microwave
cavity; positioning said sample outside said microwave cavity and
adjacent said tip; causing said tip to emit an evanescent
electromagnetic field; measuring a quality factor shift of said
probe, wherein said quality factor shift results from interaction
between said sample and said evanescent electromagnetic field; and
determining said electrical impedance and the distance between said
tip and said sample using the measured quality factor shift.
7. A method as recited in claim 6, wherein said probe comprises a
scanning evanescent microwave probe having said tip extending from
a coaxial or transmission line resonator.
8. A method as recited in claim 6, wherein said measurements of
electrical impedance are selected from the group consisting
essentially of quantitative and qualitative measurements.
9. A method as recited in claim 6, wherein said electrical
impedance comprises complex dielectric constant and conductivity of
said sample.
10. A method as recited in claim 6, wherein said sample comprises a
material selected from the group consisting essentially of
dielectric insulators, semiconductors, metallic conductors and
superconductors.
11. A method as recited in claim 6, wherein said sample comprises a
multi-layered material.
12. A method as recited in claim 11, wherein said sample comprises
a material selected from the group consisting essentially of
dielectric insulators, semiconductors, metallic conductors and
superconductors.
13. A method as recited in claim 6, wherein said tip-sample
interaction is measured with a modulated external field applied to
a backing of said sample.
14. A method as recited in claim 13, further comprising detecting
the derivatives of the resonant frequency or phase, quality factor
or amplitude of said probe with respect to modulation of said
external field using a lock-in amplifier having an operating
frequency coherent with the frequency of the modulation.
15. A method as recited in claim 13, wherein said external field
comprises a bias electric field.
16. The method as recited in claim 6, wherein the measurement is
made under quasistatic approximation conditions.
17. A method for using a scanning evanescent microwave probe to
determine electrical properties of a sample, said probe having a
tip extending from a coaxial or transmission line resonator,
comprising: measuring variation in resonant frequency and quality
factor of said resonator resulting from interaction of said tip and
said sample; said probe having said tip extending from a microwave
cavity; positioning said sample outside said microwave cavity and
adjacent but not in contact with said tip; causing said tip to emit
an evanescent electromagnetic field; scanning a surface of said
sample with said tip to measure quality factor shift of said probe,
wherein said quality factor shift results from interaction between
said sample and said evanescent electromagnetic field; and
determining electrical properties and topography of said sample
using the measured quality factor shift.
Description
INCORPORATION-BY-REFERENCE OF MATERIAL SUBMITTED ON A COMPACT
DISC
Not Applicable
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates generally to scanning probe microscopy and
more specifically to scanning evanescent electromagnetic wave
microscopy and/or spectroscopy.
2. Description of Related Art
Quantitative dielectric measurements are currently performed by
using deposited electrodes on large length scales (mm) or with a
resonant cavity to measure the average dielectric constant of the
specimen being tested. Quantitative conductivity measurements of
the test specimen can only be accurately performed with a
four-point probe. A drawback associated with performing the
aforementioned measurements is that the probe tip used to measure
the dielectric and conductivity properties of the test specimen
often comes into contact with the test specimen. Repeated contact
between the probe tip and the test specimen causes damage to both
the probe tip and the specimen, thereby making the resulting test
measurements unreliable.
Another drawback associated with the aforementioned measurements is
that gap distance between the probe tip and the test specimen can
only be accurately controlled over a milli-meter (mm) distance
range.
BRIEF SUMMARY OF THE INVENTION
The present invention allows quantitative non-contact and
high-resolution measurements of the complex dielectric constant and
conductivity at RF or microwave frequencies. The present invention
comprises methods of tip-sample distance control over dielectric
and conductive samples for the scanned evanescent microwave probe,
which enable quantitative non-contact and high-resolution
topographic and electrical impedance profiling of dielectric,
nonlinear dielectric and conductive materials. Procedures for the
regulation of the tip-sample separation in the scanned evanescent
microwave probe for dielectric and conducting materials are also
provided.
The present invention also provides methods for quantitative
estimation of microwave impedance using signals obtained by scanned
evanescent microwave probe and quasistatic approximation modeling.
The application of various quasistatic calculations to the
quantitative measurement of the dielectric constant, nonlinear
dielectric constant, and conductivity using the signal from a
scanned evanescent microwave probe are provided. Calibration of the
electronic system to allow quantitative measurements, and the
determination of physical parameters from the microwave signal is
also provided.
The present invention also provides methods of fast data
acquisition of resonant frequency and quality factor of a
resonator; more specifically, the microwave resonator in a scanned
evanescent microwave probe.
A piezoelectric stepper for providing coarse control of the
tip-sample separation in a scanned evanescent microwave probe with
nanometer step size and centimeter travel distances is
disclosed.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)
FIGS. 1(A)-1(B) are schematic views of equivalent circuits used for
modeling the tip-sample interaction;
FIG. 2 is a schematic view of the tip-sample geometry;
FIG. 3 illustrates the infinite series of image charges used to
determine the tip-sample impedance;
FIG. 4 is a graph showing the agreement between the calculated and
measure frequency shifts for variation of the tip-sample
separation.
FIG. 5 illustrates the calculation of C.sub.tip-sample;
FIG. 6 is a schematic view of the setup used to measure the
nonlinear dielectric constant;
FIG. 7 shows images of topography and .di-elect cons..sub.333 for a
periodically poled single-crystal LiNbO.sub.3 wafer;
FIG. 8 is a graph showing f.sub.r and .DELTA.(1/Q) as a function of
conductivity;
FIG. 9 illustrates the tip-sample geometry modeled;
FIG. 10 is a graph showing C.sub.r using the model
approximation;
FIG. 11 is a schematic view of the operation of the microscope for
simultaneous measurement of the topography and nonlinear dielectric
constant;
FIG. 12 shows images of topography and .di-elect cons..sub.333 for
a periodically poled single crystal LiNb0.sub.3 wafer;
FIG. 13 is a graph for the C.sub.tip-sample calculation;
FIG. 14(a)-14(b) are two graphs showing the variation of the
derivative signal versus tip-sample variation;
FIG. 15 is a graph showing calibration for regulation of tip-sample
separation;
FIG. 16 illustrates the measurement of topographic and resistivity
variations;
FIG. 17 is a schematic view of the architecture of the data
acquisition and control electronics;
FIG. 18 is a flow chart for of the architecture of the inventive
data acquisition and control electronics;
FIG. 19 illustrates the design and operation of the piezoelectric
stepper;
FIG. 20 illustrates the sequence of motion of the piezoelectric
stepper;
FIG. 21 illustrates the integration of an AFM tip with SEMM.
DETAILED DESCRIPTION OF THE INVENTION
Embodiment A
To determine quantitatively the physical properties, such as the
complex dielectric constant, nonlinear dielectric constant and
conductivity, through measurements of changes in resonant frequency
(f.sub.r) and quality factor (Q) as function of different
materials, bias electric and magnetic fields, tip-sample distance
and temperature, etc. by a scanned evanescent microwave probe
(SEMP), a quantitative model of the electric and magnetic fields in
the tip-sample interaction region is necessary. A number of
quasistatic models can be applied to the calculation of the probe
response to dielectric, nonlinear dielectric and conductive
materials. For the present invention, these models are applied to
the calculation of the complex dielectric constant, nonlinear
dielectric constant, and conductivity.
To determine the electrical properties of a sample, the variation
in resonant frequency (f.sub.r) and quality factor (Q) of a
resonant cavity is measured. (FIG. 1(A)). The tip-sample
interaction is modeled using the equivalent RLC circuit shown in
FIG. 1(B). FIG. 1(A) shows the novel evanescent probe structure
comprising a microwave resonator such as illustrated microwave
cavity 10 with coupling loops for signal input and output. The
sharpened metal tip 20, which, in accordance with the invention
acts as a point-like evanescent field emitter as well as a
detector, extends through a cylindrical opening or aperture 22 in
endwall 16 of cavity 10. Mounted immediately adjacent sharpened tip
20 is a sample 80. Cavity 10 comprises a standard quarter or half
wave cylindrical microwave cavity resonator having a central metal
conductor 18 with a tapered end 19 to which is attached sharpened
metal tip or probe 20. The tip-sample interaction appears as an
equivalent complex tip-sample capacitance (C.sub.tip-sample). Given
f.sub.r and Q, the complex tip-sample capacitance can be
extracted.
.DELTA..times..times..times..DELTA..function..times..times..times..times.-
.DELTA..times..times..times. ##EQU00001## where
.times..times.I.times..times..DELTA..times..times..DELTA..function.
##EQU00002## and f.sub.0 and Q.sub.0 are the unloaded resonant
frequency and quality factor. The calculation of C.sub.tip-sample
is described in greater detail below.
a) Modeling of the Cavity Response for Dielectric Materials
To allow the quantitative calculation of the cavity response to a
sample with a certain dielectric constant, a detailed knowledge of
the electric and magnetic fields in the probe region is necessary.
FIG. 2 describes the tip-sample geometry. The most general approach
is to apply an exact finite element calculation of the electric and
magnetic fields for a time-varying three dimensional region. This
is difficult and time consuming, particularly for the tip-sample
geometry described in FIG. 2. Since the tip is sharply curved, a
sharply varying mesh size should be implemented. Since the spatial
extent of the region of the sample-tip interaction is much less
than the wavelength of the microwave radiation used to probe the
sample (.lamda..about.28 cm at 1 GHz, .about.14 cm at 2 GHz), the
quasistatic approximation can be used, i.e. the wave nature of the
electric and magnetic fields can be ignored. This allows the
relatively easy solution of the electric fields inside the
dielectric sample. A finite element calculation of the electric and
magnetic fields under quasistatic approximation for the given
tip-sample geometry can be applied. A number of other approaches
can be employed for the determination of the cavity response with
an analytic solution, which are much more convenient to use. The
calculation of the relation between complex dielectric constant and
SEMP signals for bulk and thin film dielectric materials by means
of an image charge approach is now outlined.
Spherical Tip
i. Calculation of the Complex Dielectric Constant for Bulk
Materials.
The complex dielectric constant measured can be determined by an
image charge approach if signals from the SEMP are obtained. By
modeling the redistribution of charge when the sample is brought
into the proximity of the sample, the complex impedance of the
sample for a given tip-sample geometry can be determined with
measured cavity response (described below). A preferred model is
one that can have an analytic expression for the solution and is
easily calibrated and yields quantitatively accurate results. Since
the tip geometry will vary appreciably between different tips, a
model with an adjustable parameter describing the tip is required.
Since the region close to the tip predominately determines the
sample response, the tip as a metal sphere of radius R.sub.0 can be
modeled.
FIG. 3 illustrates the infinite series of image charges used to
determine the tip sample impedance. For dielectric samples, the
dielectric constant is largely real
.times.< ##EQU00003## where .di-elect cons..sub.r and .di-elect
cons..sub.i are the real and imaginary part of the dielectric
constant of the sample, respectively. Therefore, the real portion
of the tip-sample capacitance, C.sub.r, can be calculated directly
and the imaginary portion of the tip-sample capacitance, C.sub.i,
can be calculated by simple perturbation theory.
Using the method of images, the tip-sample capacitance is
calculated by the following equation:
.times..pi..times..times..times..times..infin..times. ##EQU00004##
where t.sub.n and a.sub.n have the following iterative
relationships:
''' ##EQU00005## with
'.times..times.' ##EQU00006## where .di-elect cons. is the
dielectric constant of the sample, .di-elect cons..sub.0 is the
permittivity of free space, d is the tip-sample separation, and R
is the tip radius.
This simplifies to:
.times..pi..times..times..times..function..function. ##EQU00007##
as the tip-sample gap approaches zero.
Since the dielectric constant of dielectric materials is primarily
real, the loss tangent (tan .delta.) of dielectric materials can be
determined by perturbation theory. The imaginary portion of the
tip-sample capacitance will be given by: C.sub.i=C.sub.r tan
.delta.. (7)
Given the instrument response, C.sub.tip-sample, the complex
tip-sample capacitance, and therefore the complex dielectric
constant of the sample can be estimated.
FIG. 4 illustrates agreement between the calculated and measure
frequency shifts for variation of the tip-sample separation. The
dielectric constant and loss tangent can be determined from
C.sub.tip-sample by a number of methods. One simple approach is to
construct a look-up table which yields the dielectric constant
corresponding to a given C.sub.tip-sample. Alternatively, it can be
directly calculated from the signals using the formula. Table 1
shows a comparison between measured and reported values for
dielectric constant and loss tangent.
The perturbed electric field inside the sample is:
.fwdarw..function..times..pi..function..times..infin..times..times..times-
..fwdarw..times..fwdarw. ##EQU00008## where q=4.pi..di-elect
cons..sub.0RV.sub.0, V.sub.0 is the voltage, and {right arrow over
(e)}.sub.r and {right arrow over (e)}.sub.z. are the unit vectors
along the directions of the cylindrical coordinates r and z,
respectively.
ii. Calculation of the Complex Dielectric Constant for Thin
Films.
The image charge approach can be adapted to allow the quantitative
measurement of the dielectric constant and loss tangent of thin
films. FIG. 5 illustrates the calculation of C.sub.tip-sample. In
the strict sense, the image charge approach will not be applicable
to thin films due to the divergence of the image charges shown in
FIG. 5. However, if the contribution of the substrate to the
reaction on the tip can be modeled properly, the image charge
approach is still a good approximation. According to the present
invention, it is expected that all films can be considered as bulk
samples if the tip is sharp enough since the penetration depth of
the field is only about R. The contribution from the substrate will
decrease with increases in film thickness and dielectric constant.
This contribution can be modeled by replacing the effect of the
reaction from the complicated image charges with an effective
charge with the following format:
.times..function..times..times. ##EQU00009## where
##EQU00010## .di-elect cons..sub.2 and .di-elect cons..sub.1 are
the dielectric constants of the film and substrate,
respectively,
##EQU00011## and d is the thickness of the film. This format
reproduces the thin and thick film limits for the signal. The
constant 0.18 was obtained by calibrating against interdigital
electride measurements at the same frequency on SrTiO.sub.3 thin
film. Following a similar process to the previous derivation,
yields:
.times..pi..times..times..times..times..infin..times..infin..times..times-
..times..function..times..times..times..times..pi..times..times..times..ti-
mes..times..infin..times..infin..times..times..times..times..times..times.-
.times..times..delta..times..times..times..times..times..times..times..tim-
es..times..delta..times..times..times..times..times. ##EQU00012##
where
##EQU00013## tan .di-elect cons..sub.2 and .di-elect cons..sub.1
are the tangent losses of the film and substrate. Table 2 lists the
results of thin film measurements using the SEMP and interdigital
electrodes at the same frequency (1 GHz).
b) Calculation of the Nonlinear Dielectric Constant
The detailed knowledge of the field distribution in Eqn. 8 allows
quantitative calculation of the nonlinear dielectric constant. The
component of the electric displacement D perpendicular to the
sample surface is given by: D.sub.3=P.sub.3+.di-elect
cons..sub.33(E.sub.l+E.sub.m)+1/2.di-elect
cons..sub.333(E.sub.l+E.sub.m).sup.2+1/6.di-elect
cons..sub.3333(E.sub.l+E.sub.m).sup.3+ . . . (12) where D.sub.3 is
the electric displacement perpendicular to the sample surface,
P.sub.3 is the spontaneous polarization, .di-elect cons..sub.ij,
.di-elect cons..sub.ijk, .di-elect cons..sub.ijkl, . . . are the
second-order (linear) and higher order (nonlinear) dielectric
constants, respectively.
Since the field distribution is known for a fixed tip-sample
separation, an estimate of the nonlinear dielectric constant from
the change in resonance frequency with applied voltage can be made.
For tip-sample separations much less than R, the signal mainly
comes from a small region under the tip where the electric fields
(both microwave electric field E.sub.m and low frequency bias
electric field E.sub.l) are largely perpendicular to the sample
surface. Therefore, only the electric field perpendicular to the
surface needs to be considered.
From Eqn. 12, the effective dielectric constant with respect to
E.sub.m can be expressed as a fraction of E.sub.1:
.function..differential..differential..function..times..function..times.
##EQU00014## and the corresponding dielectric constant change
caused by E.sub.l is:
.DELTA..times..times..times..times..times. ##EQU00015##
The change in f.sub.r for a given applied electric field E.sub.l is
related to the change in the energy stored in the cavity. Since the
electric field for a given dielectric constant is known and the
change in the dielectric constant is small, this can be calculated
by integrating over the sample:
.intg..times..DELTA..times..times..times..times..times.d.intg..times..tim-
es..times..mu..times..times..times.d.intg..times..times..times..times..tim-
es..times.d.intg..times..times..times..mu..times..times..times.d
##EQU00016## where V.sub.s is the volume of the sample containing
electric field, H.sub.0 is the microwave magnetic field, and
V.sub.t is the total volume containing electric and magnetic
fields, possibly with dielectric filling of dielectric constant
.di-elect cons.. E.sub.m is given by Eqn. 8. The application of a
bias field requires a second electrode located at the bottom of the
substrate. If the bottom electrode to tip distance is much larger
than tip-sample distance and tip radius, Eqn. 8 should also hold
for E.sub.l. The upper portion can be calculated by integrating the
resulting expression. The lower portion of the integral can be
calibrated by measuring the dependence of f.sub.r versus the
tip-sample separation for a bulk sample of known dielectric
constant. If the tip-sample separation is zero, the formula can be
approximated as:
.function..function..times..pi..times..times..times..times..times..times.-
.times..times..times..times. ##EQU00017## where V is the low
frequency voltage applied to the tip. This calculation can be
generalized in a straightforward fashion to consider the effects of
other nonlinear coefficients and thin films.
FIG. 6 illustrates the setup used to measure the nonlinear
dielectric constant. To measure .di-elect cons..sub.333, an
oscillating voltage V.sub..OMEGA., of frequency f.sub..OMEGA., is
applied to the silver backing of the sample and the output of the
mixer is monitored with a lock-in amplifier (SR 830). This bias
voltage will modulate the dielectric constant of a nonlinear
dielectric material at f.sub..OMEGA.. By measuring f.sub.r and the
first harmonic variation in the phase output simultaneously, sample
topography and .di-elect cons..sub.333 can be measured
simultaneously.
FIG. 7 shows images of topography and .di-elect cons..sub.333 for a
periodically poled single-crystal LiNbO.sub.3 wafer. The crystal is
a 1 cm.times.1 cm single crystal substrate, poled by periodic
variation of dopant concentration. The poling direction is
perpendicular to the plane of the substrate. The dielectric
constant image is essentially featureless, with the exception of
small variations in dielectric constant correlated with the
variation in dopant concentration. The nonlinear image is
constructed by measuring the first harmonic of the variation in
output of the phase detector using a lock-in amplifier. Since
.di-elect cons..sub.ijk reverses when the polarization switches,
the output of the lock-in switches sign when the domain direction
switches. The value (-2.4.times.10.sup.-19 F/V) is within 20% of
bulk measurements. The nonlinear image clearly shows the
alternating domains.
c) Calculation of the Conductivity
i. Low Conductivity
The dielectric constant of a conductive material at a given
frequency f may be written as:
.times.I.sigma. ##EQU00018## where .di-elect cons..sub.r, is the
real part of the permittivity and .sigma. is the conductivity. The
quasistatic approximation should be applicable when the wavelength
inside the material is much greater (>>) than the tip-sample
geometry. For R.sub.0.about.1 um and .lamda.=14 cm,
.apprxeq..lamda..apprxeq..times..times..times..times..times..sigma..apprx-
eq..times..times..apprxeq..times..times..OMEGA. ##EQU00019##
For .sigma.<<.sigma..sub.max, the quasistatic approximation
remains valid. C.sub.tip-sample can be calculated by the method of
images. Each image charge will be out of phase with the driving
voltage. By calculating the charge (and phase shift) accumulated on
the tip when it is driven by a voltage V, frequency f, one can
calculate a complex capacitance. For moderate tip-sample
separations, it is primarily a capacitance with a smaller real
component.
Using the method of images, we find that the tip-sample capacitance
is given by:
.times..times..pi..times..times..times..times..infin..times..times.
##EQU00020## where t.sub.n and a.sub.n have the following iterative
relationships:
''' ##EQU00021## with
'.times..times.' ##EQU00022## where .di-elect cons.=.di-elect
cons..sub.r-i.di-elect cons..sub.i is the complex dielectric
constant of the sample, .di-elect cons..sub.o is the .sub.0
permittivity of free space, d is the tip-sample separation, and R
is the tip radius.
By expressing b=b.sub.r+ib.sub.i=|b|e.sup.i.phi., the real and
complex capacitances can be separated.
.times..times..pi..times..times..times..times..infin..times..times..times-
..function..times..times..phi..times..times..times..times..times..pi..time-
s..times..times..times..infin..times..times..times..function..times..times-
..phi..times. ##EQU00023## where g.sub.1=1 and g.sub.n is given
by:
' ##EQU00024## This calculation can be generalized in a
straightforward fashion to thin films.
FIG. 8 illustrates f.sub.r and .DELTA. (1/Q) as a function of
conductivity. The curve peaks approximately where the imaginary and
real components of s become equal. For those plots, it is assumed
that the complex dielectric constant was given by
I.times..times..times..sigma. ##EQU00025##
ii. High Conductivity
For .sigma.>.sigma..sub.max, the magnetic field should also be
considered. The real portion of C.sub.tip-sample can be derived
using an image charge approach. This is identical to letting
b=1.
.times..times..pi..times..times..times..times..infin..times..times.
##EQU00026## where t.sub.n and a.sub.n have the following iterative
relationships:
''.times..times.' ##EQU00027## with
'.times..times.' ##EQU00028## where .di-elect cons. is the
dielectric constant of the sample, .di-elect cons..sub.0 is the
permittivity of free space, d is the tip-sample separation, and R
is the tip radius.
In this limit, the formula can also be reduced to a sum of
hyperbolic sines; see E. Durand, Electrostatique, 3 vol.
(1964-66).
.times..times..pi..times..times..times..times..times..times..times..infin-
..times..times..times..times. ##EQU00029## where
a=cosh.sup.-1(1+a')
The magnetic and electric fields at the surface of the conductor
are given by:
.fwdarw..function..times..times..pi..times..times..times..infin..times.'.-
times.'.times..times..fwdarw..fwdarw..function.I.times..omega..times..time-
s..pi..times..times..times..infin..times..times.'.times.'.times.'.times..t-
imes..fwdarw..PHI. ##EQU00030##
The knowledge of this field distribution allows the calculation of
the loss in the conducting sample.
Hyperbolic Tip
For tip-sample separations <R.sub.0, a spherical tip turns out
to be an excellent approximation, but the approximation does not
work well for tip-sample separations >R.sub.0. To increase the
useful range of the quasistatic model, additional modeling is
performed to accurately model the electric field over a larger
portion of the tip. An exact solution exists for a given hyperbolic
tip at a fixed distance from a conducting plane. The potential
is:
.PHI..PHI..times..function..function. ##EQU00031## The surface
charge/unit area is:
.sigma..times..times..times..pi..times..times..times..times..pi..times..-
times..times..PHI..function..times..function..function..times..times..time-
s..pi..times..times..times..PHI..function..times..function..function.
##EQU00032## The area/dy is:
.function..times..times..function..times..times.dd.times..function..funct-
ion.dd.times..times..pi..times..times..function.dd.times..times..pi..times-
..times..function..function. ##EQU00033## So, for a given v.sub.0
and a, the charge on a hyperbolic tip between y.sub.min and
y.sub.max is given by:
.times..intg..times..times..times..times..times..times..times..times..tim-
es..times..times..sigma..times.dd.times.d.times..PHI..function..times..fun-
ction..times..intg..times..times..times..times..times..times..times..times-
..times..times..times.d.function..function..times..PHI..times..times..time-
s..function..function..function..times..times..times..times..times..times.-
.times. ##EQU00034## Given proper choice of the limits of
integration and tip parameters, Eq. 34 may be used to more
accurately model the tip-sample capacitance as detailed below.
iii. Large Tip-Sample Separations
The long-range dependence is modeled by calculating
C.sub.tip-sample. For large tip-sample separations, there is no
problem. (separations roughly>tip radius). The capacitance is
calculated as the sum of the contribution from a cone and a
spherical tip. For the cone, the charge only outside the tip radius
is considered. This solution can be approximately adapted to a
variable distance. FIG. 9 describes the tip-sample geometry
modeled; where:
Tip radius: R.sub.0
Opening angle: .theta.
Wire radius: R.sub.wire
Tip-sample separation: x.sub.0
To approximate the contribution of the conical portion of the tip
to the tip-sample capacitance, the conical portion of the tip is
divided into N separate portions, each portion n extending from
y.sub.n-1 to y.sub.n. For each portion, the hyperbolic parameters
(a, v.sub.0) are found for which the hyperbola intersects and is
tangent to the center of the portion.
Given points x, y on a hyperbola, and the slopes, find the
hyperbola intersecting
and tangent to point (x, y). x=av(u.sup.2+1).sup.1/2 (35)
y=au(1-v.sup.2).sup.1/2 (36) Eliminate u.
.function..times.dd.times..times..times..times..times. ##EQU00035##
Eliminate a. From Derivative Equation:
.times..function. ##EQU00036##
Substitute into Equation for Hyperbola:
.times..function..times..times..function..times..function..function..time-
s. ##EQU00037## get a from above. Finally, the charges accumulated
on each portion of the tip are summed and a capacitance is
obtained.
The contribution from each conical portion of the tip is given
approximately by:
.times..times..function..function..function. ##EQU00038## where
C.sub.n.sub.cone-sample is the contribution to the tip-sample
capacitance from the nth portion of the cone.
Assuming N equally spaced cone portions, for the sphere+cone tip
modeled,
here:
.times..times..theta..function..times..times. ##EQU00039## The
total tip-sample capacitance is then given by the sum of the
portions of the cone and the spherical portion of the tip,
C.sub.sphere-sample, as given by Eq. 24. (C.sub.sphere-sample is
substituted for C.sub.tip-sample to reduce confusion.)
.times. ##EQU00040##
For small tip-sample separations, this model does not work well. So
the capacitance is calculated using the spherical model (which
dominates) and the line tangent to the contribution from the cone
is made. FIG. 10 shows C.sub.r using this approximation.
Embodiment B
The above described models are applied to the regulation of the
tip-sample separation for dielectric and conductive materials. In
principle, with above models, the relationship between tip sample
distance, electrical impedance and measured signals (f.sub.r and Q
as function of sample difference, bias fields and other variables)
is known precisely, at least when the tip is very close to the
sample. If measured f.sub.r and Q signal points (and their
derivatives with respect to electric or magnetic fields, distance
and other variables) are more than unknown parameters, the unknowns
can be uniquely solved. If both tip-sample distance and electrical
impedance can be determined simultaneously, then the tip-sample
distance can be easily controlled, so that the tip is always kept
above the sample surface with a desired gap (from zero to microns).
Both topographic and electrical impedance profiles can be obtained.
The calculation can be easily performed by digital signal processor
or any computer in real time or after the data acquisition.
Since the physical properties are all calculated from the f.sub.r
and Q and their derivatives, the temperature stability of the
resonator is crucial to ensure the measurement reproducibility. The
sensitivity very much depends on the temperature stability of the
resonator. Effort to decrease the temperature variation of
resonator using low thermal-coefficient-ceramic materials to
construct the resonator should be useful to increase the
sensitivity of the instrument.
d) Tip-Sample Distance Control for Dielectric Materials
i.) For Samples of Constant Dielectric Constant, the Tip-Sample
Separation can be Regulated by Measurement of f.sub.r.
Other physical properties, i.e. nonlinear dielectric or loss
tangent can be measured simultaneously.
FIG. 11 illustrates the operation of the microscope for
simultaneous measurement of the topography and nonlinear dielectric
constant. From the calibration curve of resonant frequency versus
tip-sample separation, a reference frequency fret is chosen to
correspond to some tip-sample separation. To regulate the
tip-sample distance, a phase-locked loop (FIG. 11) is used. A
microwave signal of frequency fret is input into the cavity 10,
with the cavity output being mixed with a signal coming from a
reference path. The length of the reference path is adjusted so
that the mixed output is zero when the resonance frequency of the
cavity matches f.sub.ref. The output of the phase detector 41 is
fed to an integrator 44, which regulates the tip-sample distance by
changing the extension of a piezoelectric actuator 50 (Burleigh
PZS-050) to maintain the integrator output near zero. For samples
with uniform dielectric constant, this corresponds to a constant
tip-sample separation. To measure .di-elect cons..sub.333, an
oscillating voltage V.sub..OMEGA., of frequency f.sub..OMEGA., is
applied to the silver backing of the sample and the output of the
phase detector is monitored with a lock-in amplifier (SR 830). This
bias voltage will modulate the dielectric constant of a nonlinear
dielectric material at f.sub..OMEGA.. Since f.sub..OMEGA. exceeds
the cut-off frequency of the feedback loop, the high frequency
shift in c from V.sub..OMEGA. does not affect the tip-sample
separation directly. By measuring the applied voltage to the
piezoelectric actuator and the first harmonic variation in the
phase output simultaneously, sample topography and .di-elect
cons..sub.333 can be measured simultaneously.
FIG. 12 shows images of topography and for a periodically poled
single-crystal LiNbO.sub.3 wafer. The crystal is a 1 cm.times.1 cm
single crystal substrate, poled by application of a spatially
periodic electric field. The poling direction is perpendicular to
the plane of the substrate. The topographic image is constructed by
measuring the voltage applied to the piezoelectric actuator. It is
essentially featureless, with the exception of a constant tilt and
small variations in height correlated with the alternating domains.
The small changes are only observable if the constant tilt is
subtracted from the figure. Since .di-elect cons..sub.ijk is a
third-rank tensor, it reverses sign when the polarization switches,
providing an image of the domain structure. The nonlinear image is
constructed by measuring the first harmonic of the variation in
output of the phase detector using a lock-in amplifier. Since
.di-elect cons..sub.ijk reverses when the polarization switches,
the output of the lock-in switches sign when the domain direction
switches. The value (-2.4.times.10.sup.-19 F/N) is within 20% of
bulk measurements. The nonlinear image clearly shows the
alternating domains.
Ferroelectric thin films, with their switchable nonvolatile
polarization, are also of great interest for the next generation of
dynamic random access memories. One potential application of this
imaging method would be in a ferroelectric storage media. A number
of instruments based on the atomic force microscope have been
developed to image ferroelectric domains either by detection of
surface charge or by measurement of the piezoelectric effect. The
piezoelectric effect, which is dependent on polarization direction,
can be measured by application of an alternating voltage and
subsequent measurement of the periodic variation in sample
topography. These instruments are restricted to tip-sample
separations less than 10 nanometers because they rely on
interatomic forces for distance regulation, reducing the possible
data rate. Since the inventive microscope measures variations in
the distribution of an electric field, the tip-sample separation
can be regulated over a wide range (from nanometers to
microns).
ii.) For Samples with Varying Dielectric Constant, f.sub.r Changes
with .di-elect cons..
To extract the dielectric constant and topography simultaneously,
an additional independent signal is required. This can be
accomplished in several ways:
1. Measuring more than one set of data for f.sub.r and Q at
different tip-sample distances. This method is especially effective
when the tip-sample distance is very small. The models described in
Embodiment A can then be used to determine the tip-sample distance
and electrical impedance through DSP or computer calculation. In
this approach, as the tip is approaching the sample surface the DSP
will fit the tip-sample distance, dielectric constant and loss
tangent simultaneously. These values should converge as the
tip-sample distance decreases. Therefore, this general approach
will provide a true non-contact measurement mode, as the tip can
kept at any distance away from the sample surface as long as the
sensitivity (increase as tip-sample distance decreases) is enough
for the measurement requirement. This mode is referred to as
non-contact tapping mode. During the scanning, at each pixel the
tip is first pull back to avoid crash before lateral movement. Then
the tip will approach the surface as DSP calculate the dielectric
properties and tip-sample distance. As the measurement value
converge to have less error than specified or calculated tip-sample
distance is less than a specified value, the tip stop approaching
and DSP record the final values for that pixel. In this approach, a
consistent tip-sample moving element is critical, i.e. the element
should have a reproducible distance vs, e.g. control voltage.
Otherwise, it increases the fitting difficulty and measurement
uncertainty. This requirement to the z-axis moving element may be
hard to satisfy. An alternative method is to independently encode
the z-axis displacement of the element. Capacitance sensor and
optical interferometer sensor or any other distance sensor can be
implemented to achieve this goal.
2. In particular, when the tip is in soft contact (only elastic
deformation is involved) to the surface of the sample, there will
be a sharp change in the derivatives of signals (fr and Q) as
function of approaching distance. This method is so sensitive that
it can be used to determine the absolute zero of tip-sample
distances without damaging the tip. Knowing the absolute zero is
very useful and convenient for further fitting of the curve to
determine the tip-sample distance and electrical impedance. A soft
contact "tapping mode" (as described in above) can be implemented
to perform the scan or single point measurements. The approaching
of tip in here can be controlled at any rate by computer or DSP. It
can be controlled interactively, i.e. changing rate according to
the last measurement point and calculation.
3. The method described in 1) can be alternatively achieved by a
fixed frequency modulation in tip-sample distance and detected by a
lock-in amplifier to reduce the noise. The lock-in detected signal
will be proportional to the derivative of fr and Q as function of
tip-sample distance. A sharp decrease in this signal can be used as
a determination of absolute zero (tip in soft contact with sample
surface without damaging the tip). Using relationships described in
Embodiment A, any distance of tip-sample can be maintained within a
range that these relationship is accurate enough.
Details
At a single tip-sample separation, the microwave signal is
determined by the dielectric constant of the sample. However, the
microwave signal is a fraction of both the tip-sample separation
and the dielectric constant. Thus, the dielectric constant and
tip-sample separation can be determined simultaneously by the
measurement of multiple tip-sample separations over a single point.
Several methods can be employed to achieve simultaneous measurement
of tip-sample separation and dielectric constant. First, the
derivative of the tip-sample separation can be measured by varying
the tip-sample separation. Given a model of the tip-sample
capacitance, (Eqn. 3), the tip-sample separation and dielectric
constant can then be extracted. The dependence on tip-sample
separation and dielectric constant can be modeled using a modified
fermi function.
.times..pi..times..times..times..times..times..times..times..times..funct-
ion..function..times..times.'.function. ##EQU00041## where
b=(.di-elect cons.-.di-elect cons..sub.0)/(.di-elect
cons.+.di-elect cons..sub.0). Furthermore, G(.di-elect cons.) and
x.sub.0(.di-elect cons.) can be fitted well with rational functions
as:
.function..times..times..times..times..times..times..times..times..times.-
.function..times..times..times..times..times..times..times..times..times.
##EQU00042## FIG. 13 illustrates the agreement between Eqn. 3 and
Eqn. 43.
Equation 43 is suitable for rapid calculation of the tip-sample
separation and dielectric constant. The tip-sample separation and
dielectric constant can also be extracted by construction of a
look-up table. The architecture described in f) below is then used
to regulate the tip-sample separation. FIG. 14a and FIG. 14b show
the variation of the derivative signal versus tip-sample variation.
FIG. 14a is modeled assuming a 10 .mu.m spherical tip. FIG. 14b is
a measured curve. Maintaining the tip-sample separation at the
maximum point of the derivative signal can also regulate the
tip-sample separation. This has been demonstrated by scanning the
tip-sample separation and selecting the zero slope of the
derivative signal. It can also be accomplished by selecting the
maximum of the second harmonic of the microwave signal.
e) Tip-Sample Distance Control for Conductive Materials
For conductive materials, the tip-sample separation and microwave
resistivity can be measured simultaneously in a similar fashion.
Since Eqn. 24 is independent of conductivity for good metals,
C.sub.tip-sample can be used as a distance measure and control.
This solution should be generally applicable to a wide class of
scanned probe microscopes that include a local electric field
between a tip and a conducting sample. It should prove widely
applicable for calibration and control of microscopes such as
scanning electrostatic force and capacitance microscopes.
From the calibration curves, a frequency f.sub.ref is chosen to
correspond to some tip sample separation (FIG. 15). The tip-sample
separation is then regulated to maintain the cavity resonance
frequency at f.sub.ref. This can be accomplished digitally through
the use of the digital signal processor described in f) below. An
analog mechanism can and has also been used. A phase-locked loop
described in FIG. 11 has also been used to regulate the tip-sample
separation. FIG. 16(a)(c) illustrate the measurement of topography
with constant microwave conductivity. FIG. 16(b)(d) illustrate the
measurement of conductivity variations.
This method allows submicron imaging of the conductivity over large
length scales. This method has the advantage of allowing distance
regulation over a wide length scale (ranging from microns to
nanometers) giving rise to a capability analogous to the optical
microscope's ability to vary magnification over a large scale.
Force Sensor Distance Feedback Control
In many cases, an absolute and independent determination of
zero-distance is desirable as other methods can rely on model
calculations and require initial calibration and fitting. A method
that relies on measuring the vibration resonant frequency of the
tip as a force sensor has been implemented. When the tip approaches
the sample surface, the mechanical resonant frequency of the tip
changes. This change can be used to control the tip-sample
distance. This approach has been shown to be feasible and that this
effect does exist. This effect has been found to exist over a very
long range (.about.1 micron). The long-range effect is believed to
come from the electrostatic force and the short-range effect is
from a shear force or an atomic force. A low frequency DDS-based
digital frequency feedback control electronics system similar to
the microwave one discussed above is implemented to track the
resonant frequency and Q of this mechanical resonator. The measure
signals will then be used to control the distance. This is similar
to shear force measurement in near field scanning microscope
(NSOM). The signal is derived from the microwave signal, not from
separate optical or tuning fork measurements as in other methods.
This feature is important since no extra microscope components are
required. The electronics needed is similar to the high frequency
case. This features is critical for high-resolution imaging and
accurate calibration of the other two methods.
Integration of AFM
It is very useful to integrate an atomic force microscope (AFM) tip
with SEMM in some applications where a high-resolution topography
image is desirable. The tip resonant frequency (10 kHz) and quality
factor limit the bandwidth of shear force feedback in closed loop
applications. Previously, in a scanning capacitance microscope
(SCM), an AFM tip has been connected to a microwave resonator
sensor to detect the change in capacitance between the tip and the
bottom electrode. In principle, SCM is similar to our SEMM.
However, insufficient coupling between the tip and resonator, very
large parasitic capacitance in the connection, and lack of
shielding for radiation prevented the SCM from having any
sensitivity in direct (dc mode) measurements of the tip-sample
capacitance without a bottom electrode and ac modulation. (SCM only
can measure dC/dV).
A new inventive design will allow easy integration of an AFM tip to
the SEMM without losing the high sensitivity experienced with the
SEMM. This new design is based on a modification stripline
resonator with the inventors' proprietary tip-shielding structure
(see FIG. 21). Since the AFM tip is connected within less than 1 mm
of the central strip line, the sensitivity will not be reduced
seriously and parasitic capacitance with be very small (shielding
also reduces the parasitic capacitance). The AFM tip is custom
designed to optimize the performance. With this unique inventive
design, nanometer resolution can be achieved in both topography and
electrical impedance imaging, which is critical in gate oxide
doping profiling and many other applications.
Embodiment C
By contrast to most types of microscope, SEMM measures a complex
quantity, i.e., the real and imaginary parts of the electrical
impedance. This is realized by measuring the changes in the
resonant frequency (f.sub.r) and quality factor (Q) of the
resonator simultaneously. A conventional method of measuring these
two quantities is to sweep the frequency of the microwave generator
and measure the entire resonant curve. For each measurement, this
can take seconds to minutes depending on the capabilities of the
microwave generator. These measurements are limited by the
switching speed of a typical microwave generator to roughly 20 Hz.
With the use of a fast direct digital synthesizer based microwave
source, the throughput can be improved to roughly 10 kHz, but is
still limited by the need to switch over a range of frequencies.
Another method is to implement an analog phase-locked loop for
frequency feedback control. This method can track the changing
resonant frequency in real time and measure f.sub.r and Q quickly.
However, one has to use a voltage-controlled-oscillator (VCO) as a
microwave generator which usually only has a frequency stability of
10.sup.-4. This low frequency stability will seriously degrade the
sensitivity of the instrument. Since .DELTA..di-elect
cons./.di-elect cons..about.500.DELTA.f.sub.r/f.sub.r, frequency
instability in the VCO will limit measurement accuracy. Another
problem is that interaction between this frequency feedback loop
and the tip-sample distance feedback loop can cause instability and
oscillation, which will seriously limit the data rate.
A direct digital synthesizer (DDS) based microwave generator is
used to implement the method according to the present invention. In
a preferred embodiment, the DSS has a frequency stability of better
than 10.sup.-9. The inventive method fixes the frequency of the
microwave signal at the previous resonant frequency and measures
I/Q signals simultaneously. Since the microwave frequency is fixed,
the DDS switching speed does not limit the data rate. By measuring
the in-phase and quadrature microwave signals, the inventors can
derive f.sub.r and Q. Near resonance, the in-phase and quadrature
signals are given by: i=A sin .theta.
Q=A cos .theta., where A is the amplitude of the microwave signal
on resonance and .theta. is the phase shift of the transmitted
wave. Given i, q, the current input microwave frequency, and the
input coupling constants, the current f.sub.r and Q can be
calculated. For a resonator with initial quality factor Q.sub.0,
transmitted power A.sub.0, and resonant frequency f.sub.0, driven
at frequency f,
.DELTA..times..times..times..times..times..theta..times..times..times..ti-
mes..times..times..times..times..times..theta..times..DELTA..times..times.
##EQU00043## .times..times..times..times..times..theta.
##EQU00043.2## where
.smallcircle..smallcircle..smallcircle. ##EQU00044## Then, f.sub.r
and Q can be obtained by
.times..times..times. ##EQU00045## .times..times.
##EQU00045.2##
Initially, since the I/Q mixer does not maintain perfect phase or
amplitude balance, these quantities are calibrated. To calibrate
the relative amplitudes at a given frequency of the i and q outputs
of the mixer, the relative values of the outputs are measured when
the reference signal is shifted by 90 degrees. This can easily be
extended by means of a calibration table.
To calibrate the relative phases of the i and q outputs at a given
frequency, the i output of the mixer is measured on resonance. At
resonance,
i/q=.delta., where .delta. is the phase error of the I/Q mixer.
Near Resonance,
.times..times..times..times..times..theta..delta..times..times..times..ti-
mes..times..theta..times..times..times..times..delta..times..times..times.-
.times..times..delta..times..times..times..times..theta..times..times..tim-
es..times..times..theta..times..times..delta..times..times..times..times..-
theta..times..times..times..times..times..theta..times..times..times..delt-
a. ##EQU00046## This allows the correction of the phase error of
the mixer.
This method of measurement only requires one measurement cycle.
Therefore, it is very fast and limited only by the DSP calculation
speed. To increase the working frequency range, the DSP is used to
control the DDS frequency to shift when the resonant frequency
change is beyond the linear range. This method allows data rates
around 100 kHz-1 MHz (limited by the bandwidth of the resonator)
and frequency sensitivity below 1 kHz
.DELTA..times..times..apprxeq..times..times..times..times.
##EQU00047##
f) Data Acquisition and Control Electronics
FIGS. 17 and 18 illustrate the architecture of the inventive data
acquisition and control electronics. FIG. 17 contains a schematic
for the EMP. FIG. 18 is a flow chart describing the operation of
the SEMP.
To eliminate the communication bottleneck between data acquisition,
control electronics and the computer, the high performance PCI bus
is adopted for every electronic board. A main board with four
high-speed digital signal processors (DSPs) is used to handle data
acquisition, feedback control loops and other control functions
separately. Four input data signals (A/Ds) and six control signals
(D/As) were implemented.
The input signals include:
1) in-phase (I=A sin .theta., where A is the amplitude and .theta.
the phase) signal,
2) quadrature (q=A cos .theta.) signal,
3) in-phase signal of tip vibration resonant frequency or tapping
mode signal electric/magnetic/optical field modulations,
4) quadrature signal of tip vibration resonance,
The output signals include:
1-3) fine x-y-z piezo-tube control signals,
4) z-axis coarse piezo-step-motor signal,
5-6) coarse x-y stage signals.
The DSPs are dedicated to specific functions as follows:
DSP1: microwave frequency f.sub.r and Q data acquisition,
DSP2: tip mechanical resonant frequency f.sub.m and Q.sub.m or
microwave derivative signal data acquisition,
DSP3: tip-sample distance feedback control,
DSP4: x-y fine/coarse scan and image data acquisition,
The division of labor between a number of fast processors
simplifies design and allows rapid processing of multiple tasks. A
fast system bus is necessary to allow rapid transfer of data to the
display and between neighboring boards.
Stepping Motor--Coarse Positioning
Embodiment D
For all scanned probe microscopes, increasing resolution decreases
the measurable scan range. Microscopes must be able to alter their
scan position by millimeters to centimeters while scanning with
high resolution over hundreds of microns. Given samples of
macroscopic scale, means must exit to adjust the tip-sample
separation over macroscopic (mm) distances with high stability over
microscopic distances (nm). Conventional piezoelectric positioners
are capable only of movements in the range of hundreds of microns
and are sensitive to electronic noise even when stationary. In
addition, they are subject to large percentage drifts. (>1% of
scan range) As such, separate means of coarse and fine adjustment
of position are necessary. A coarse approach inventive mechanism by
means of a novel piezoelectric stepper motor has been designed to
accomplish this.
FIG. 19 illustrates the design and operation of the stepper motor.
The cross-sectional view illustrates that the motor consists of a
sapphire prism in the form of an equilateral triangle clamped into
an outer casing. There are 3 Piezoelectric stacks topped by a thin
sapphire plate contact each side of the prism. Each piezoelectric
stack consists of a lower expansion plate, which is used to grip
and release the prism, an upper shear plate, which is used to move
the prism, and a thin sapphire plate, which is used to provide a
uniform surface. FIG. 20 shows the sequence of motion. At step (a),
the motor is stationary. At step (b), a smooth rising voltage is
applied to each shear place and the center prism moves. At step
(c), the voltage to the expansion plates labeled (2) is reduced.
This reduces the pressure applied by those plates and thus the
frictional force. The center points the motor fixed. At step (d),
the voltage to the shear plates labeled (1) is reduced. Since the
plates have been retracted, the friction between these plates and
the prism is reduced, letting the center plates hold the prism. At
step (e), the voltage to the expansion plates labeled (2) is
increased, increasing the pressure applies by the other plates. At
step (F), the voltage to the expansion plates labeled (4) is
reduced. The outer points hold the motor fixed. At step (g), the
voltage to the shear plates labeled (3) is reduced. At step (h),
the voltage to the expansion plates labeled (4) is increased,
restoring the pressure applied by the center points to its original
value. This motor has a number of advantages by comparison to
earlier designs. Prior designs had only 2 piezoelectric elements
per side and relied on a stick-slip motion, similar to pulling a
tablecloth from under a wineglass. The use of a third piezoelectric
element on each side and the addition of an expansion piezoelectric
have several benefits. First, since the method of motion does not
involve slip-stick, it is less prone to vibration induced by the
necessary sharp motions. Second, the requirements for extreme
cross-sectional uniformity of the central element are reduced by
the use of the expansion piezoelectric plates.
While the present invention has been particularly described with
respect to the illustrated embodiment, it will be appreciated that
various alterations, modifications and adaptations may be made
based on the present disclosure, and are intended to be within the
scope of the present invention. While the invention has been
described in connection with what is presently considered to be the
most practical and preferred embodiments, it is to be understood
that the present invention is not limited to the disclosed
embodiments but, on the contrary, is intended to cover various
modifications and equivalent arrangements included within the scope
of the appended claims.
TABLE-US-00001 TABLE 1 Single Crystal Measurement Measured Reported
Measured Reported Material .epsilon..sub.r .epsilon..sub.r
tan.delta. tan.delta. YSZ 30.0 29 1.7 .times. 10.sup.-3 1.75
.times. 10.sup.-3 LaGaO.sub.3 23.2 25 1.5 .times. 10.sup.-3 1.80
.times. 10.sup.-3 CaNdAlO.sub.4 18.2 ~19.5 1.5 .times. 10.sup.-3
0.4-2.5 .times. 10.sup.-3 TiO.sub.2 86.8 85 3.9 .times. 10.sup.-3
.sup. 4 .times. 10.sup.-3 BaTiO.sub.3 295 300 0.47 0.47 YAlO.sub.3
16.8 16 -- 8.2 .times. 10.sup.-5 SrLaAlO.sub.4 18.9 20 -- --
LaALO.sub.3 25.7 24 -- 2.1 .times. 10.sup.-5 MgO 9.5 9.8 -- 1.6
.times. 10.sup.-5 LiNbO.sub.3 32.0 30 -- -- (X-cut)
TABLE-US-00002 TABLE 2 @Interdigital SEMM (1 GH.sub.z) Electrodes
(1 GH.sub.z) Films .epsilon..sub.r tan.delta. .epsilon..sub.r
tan.delta. Ba.sub.0.7Sr.sub.0.3TiO.sub.3 707 0.14 750 0.07
Ba.sub.0.5Sr.sub.0.5TiO.sub.3 888 0.19 868 0.10 SrTiO.sub.3 292
0.02 297 0.015 Ba.sub.0.24Sr.sub.0.35Ca.sub.0.41TiO.sub.3 150 0.05
*Ba.sub.0.25Sr.sub.0.35Ca.sub.0.4TiO.sub.3 240 0.05 @Measurement by
S. Kirchoefer and J. Pond, NRL also consistent with results by NIST
group *Film made by H. Jiang and V. Fuflyigin, NZ Applied
Technology Loss values are higher since we are more sensitive to
surface.
* * * * *